# §23.4 Graphics

## §23.4(i) Real Variables

Line graphs of the Weierstrass functions $\wp\left(x\right)$, $\zeta\left(x\right)$, and $\sigma\left(x\right)$, illustrating the lemniscatic and equianharmonic cases. (The figures in this subsection may be compared with the figures in §22.3(i).) Figure 23.4.1: ℘⁡(x;g2⁡,0) for 0≤x≤9, g2⁡ = 0.1, 0.2, 0.5, 0.8. (Lemniscatic case.) Magnify Figure 23.4.2: ℘⁡(x;0,g3⁡) for 0≤x≤9, g3⁡ = 0.1, 0.2, 0.5, 0.8. (Equianharmonic case.) Magnify Figure 23.4.4: ζ⁡(x;0,g3⁡) for 0≤x≤8, g3⁡ = 0.1, 0.2, 0.5, 0.8. (Equianharmonic case.) Magnify Figure 23.4.6: σ⁡(x;0,g3⁡) for -5≤x≤5, g3⁡ = 0.1, 0.2, 0.5, 0.8. (Equianharmonic case.) Magnify

## §23.4(ii) Complex Variables

Surfaces for the Weierstrass functions $\wp\left(z\right)$, $\zeta\left(z\right)$, and $\sigma\left(z\right)$. Height corresponds to the absolute value of the function and color to the phase. See also About Color Map. (The figures in this subsection may be compared with the figures in §22.3(iii).) Figure 23.4.8: ℘⁡(x+i⁢y) with ω1=K⁡(k), ω3=i⁢K′⁡(k) for -2⁢K⁡(k)≤x≤2⁢K⁡(k), 0≤y≤6⁢K′⁡(k), k2=0.9. (The scaling makes the lattice appear to be square.) Magnify 3D Help Figure 23.4.10: ζ⁡(x+i⁢y;1,0) for -5≤x≤5, -5≤y≤5. Magnify 3D Help Figure 23.4.12: ℘⁡(3.7;a+i⁢b,0) for -5≤a≤3, -4≤b≤4. There is a double zero at a=b=0 and double poles on the real axis. Magnify 3D Help